It took a while to drum up the courage, but I am now running Bullseye:
$ cat /etc/os-release
PRETTY_NAME="Raspbian GNU/Linux 11 (bullseye)"
A user error caused me to upgrade to Buster (from Stretch) before doing it all again to get to Bullseye.
As near as I can tell, the only thing that broke was
mosquitto because the the version I was running allowed external connections by default and the newest version doesn't. Two lines in the configuration file later, everything started working again. PiHole didn't miss a beat because I kept several of the PiHole-related config files during the upgrade(s).
Then I ran the script to install NR and after the first failure I specified
--node12 it ran through to completion without error. I was scared to go higher than 12, someone can chime in and tell me whether I should upgrade to 14 or 16.
Now I am 100% up to date! The latest NR looks great.
Thanks for the advice.